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Edited
Ponies generally probably use bases 2, 4 and 8 regularly. Base 2 for money (bits), 4 for hoof-countable things, 8 for time.
Just a silly little headcanon.
Well, the only way I can think of to reconcile “Family Appreciation Day” with Twilight’s “Centuries” line in “Winter Wrap-Up” is if ponies count in base 4.